cos 30°
√3/ 2
cos 30° is equal to √3/2 or approximately 0.866.
To arrive at this answer, we can use the fact that cosine is the ratio of the adjacent side to the hypotenuse in a right-angled triangle. In a 30-60-90 degree triangle, the cosine of 30 degrees is equal to the length of the side adjacent to the 30-degree angle, divided by the length of the hypotenuse.
We can construct this triangle by drawing an equilateral triangle (a triangle with all sides equal) and then drawing a perpendicular line from one of the vertices to the opposite side, dividing the equilateral triangle into two 30-60-90 degree triangles.
In this triangle, the hypotenuse (the longest side opposite the right angle) is 2 units (because it is twice the length of the side opposite the 30-degree angle), and the adjacent side (the shorter side next to the 30-degree angle) is √3 units (because it is the square root of 3, which is the length of the opposite side divided by 2). Therefore, the cosine of 30 degrees is :
cos 30° = adjacent side / hypotenuse
cos 30° = √3 / 2
or approximately 0.866.
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